dirichlet_params {dampack} | R Documentation |
Calculate alpha parameters of Dirichlet distribution.
Description
Function to calculate the \alpha
parameters of the Dirichlet distribution
based on the method of moments (MoM) using the mean \mu
and standard
deviation \sigma
of the random variables of interest.
Usage
dirichlet_params(p.mean, sigma)
Arguments
p.mean |
Vector of means of the random variables. |
sigma |
Vector of standard deviation of the random variables (i.e., standard error). |
Value
numeric vector of method-of-moment estimates for the alpha parameters of the dirichlet distribution
Details
Based on methods of moments. If \mu
is a vector of means and
\sigma
is a vector of standard deviations of the random variables, then
the second moment X_2
is defined by \sigma^2 + \mu^2
. Using the
mean and the second moment, the J
alpha parameters are computed as follows
\alpha_i = \frac{(\mu_1-X_{2_{1}})\mu_i}{X_{2_{1}}-\mu_1^2}
for i = 1, \ldots, J-1
, and
\alpha_J = \frac{(\mu_1-X_{2_{1}})(1-\sum_{i=1}^{J-1}{\mu_i})}{X_{2_{1}}-\mu_1^2}
References
Fielitz BD, Myers BL. Estimation of parameters in the beta distribution. Dec Sci. 1975;6(1):1–13.
Narayanan A. A note on parameter estimation in the multivariate beta distribution. Comput Math with Appl. 1992;24(10):11–7.
Examples
p.mean <- c(0.5, 0.15, 0.35)
p.se <- c(0.035, 0.025, 0.034)
dirichlet_params(p.mean, p.se)